Question: Solve for $x$ and $y$ using elimination. ${-5x-y = -51}$ ${-2x+y = -19}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-7x = -70$ $\dfrac{-7x}{{-7}} = \dfrac{-70}{{-7}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-5x-y = -51}\thinspace$ to find $y$ ${-5}{(10)}{ - y = -51}$ $-50-y = -51$ $-50{+50} - y = -51{+50}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {-2x+y = -19}\thinspace$ and get the same answer for $y$ : ${-2}{(10)}{ + y = -19}$ ${y = 1}$